Question 1

Which formula is used to find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in the rectangular coordinate system?

Accepted Answer

$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Question 2

Given the points $A(2, 3)$ and $B(8, 7)$, what is the midpoint of the line segment connecting them?

Accepted Answer

$(5, 5)$

Question 3

A biologist tracks the movement of a tagged animal from $(1, 2)$ to $(4, 6)$. What is the straight-line distance the animal traveled?

Accepted Answer

$\sqrt{9 + 16}$

Question 4

Which of the following is the correct equation for the graph of a line passing through $(0, 0)$ and $(2, 4)$?

Accepted Answer

$y = 2x$

Question 5

A city planner wants to find the midpoint between two locations at $(3, 8)$ and $(9, 2)$. What is the midpoint?

Accepted Answer

$(6, 5)$

Question 6

If the distance between $(x_1, y_1)$ and $(x_2, y_2)$ is $10$, and $x_1 = 1$, $y_1 = 2$, $x_2 = 7$, what is $y_2$?

Accepted Answer

$y_2 = 8$

Question 7

Which of the following points lies on the line $y = 3x - 2$?

Accepted Answer

$(1, 1)$

Question 8

A runner starts at $(0, 0)$ and finishes at $(6, 8)$. What is the total distance covered if the runner moves in a straight line?

Accepted Answer

$\sqrt{36 + 64}$

Question 9

Which formula gives the midpoint $M$ of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$?

Accepted Answer

$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Question 10

A chemist plots the temperature change over time and gets the equation $y = 5x + 3$. What is the $y$-intercept of this graph?

Accepted Answer

$3$

Question 11

If the endpoints of a segment are $(-2, 4)$ and $(6, -8)$, what is the distance between them?

Accepted Answer

$\sqrt{(6 - (-2))^2 + (-8 - 4)^2}$

Question 12

A medical researcher records patient data at $(5, 12)$ and $(13, 4)$. What is the midpoint of these two data points?

Accepted Answer

$(9, 8)$

Question 13

Which of the following equations represents a line with slope $-2$ and $y$-intercept $5$?

Accepted Answer

$y = -2x + 5$

Question 14

A surveyor measures two points: $(7, 3)$ and $(2, 11)$. What is the distance between them?

Accepted Answer

$\sqrt{(7 - 2)^2 + (3 - 11)^2}$

Question 15

Which of the following is NOT a correct way to graph an equation in the rectangular coordinate system?

Accepted Answer

Ignoring the relationship between $x$ and $y$

Fundamental Concepts in the Rectangular Coordinate System

Study Guide - Practice Questions